Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. M32×D197 | C2 | semidirect |
| 3. #27161114 | C2 | semidirect |
| 4. #27160890 | C2 | semidirect |
| 5. #27160889 | C2 | semidirect |
| 6. #27160888 | C2 | semidirect |
| 7. #360×C197 | C2 | semidirect |
| 9. #20263349 | C4 | semidirect |
| 13. #20263345 | C4 | semidirect |
| 14. Q16×D197 | C4 | semidirect |
| 16. D8×D197 | C4 | semidirect |
| 19. #20263266 | C22 | semidirect |
| 23. #20263258 | C22 | semidirect |
| 25. M32×C197 | C22 | semidirect |
| 26. #106×C197 | C22 | semidirect |
| 110. C197 | #2145 | semidirect |
| 118. #360 | D197 | semidirect |
| 133. M32 | C2×D197 | semidirect |
| 137. #106 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D197 | 2 |
| M32×D197 | 2 |
| #27161114 | 2 |
| #27160890 | 2 |
| #27160889 | 2 |
| #27160888 | 2 |
| #360×C197 | 2 |
| #2145 | 197 |